TA 

7^f 



NIVERSITY OF ILLINOIS BULLETIN 

Issued Weekly 

A. XVIII April 25, 1921 No. 34 

[Entered as second-class matter December 11, 1912, at the post office at Urbana, Illinois, under the 

Act of August 24, 1912. Acceptance for mailing at the special rate of postage provided 

for In section 1103, Act of October 3, 1917, authorized July 31, 19181 



THE THERMAL CONDUCTIVITY AND 
DIFFUSIVITY OF CONCRETE 

BY 

A. P. CARMAN 

AND ' 

R. A. NELSON 




BULLETIN No. 122 
ENGINEERING EXPERIMENT STATION 

Published bt the University of Illinois, Urbana 



Price: Twenty Cents 

European Agent 

Chapman & Hall, Ltd., London 



THE Engineering Experiment Station was established by act of 
the Board of Trustees of the University of Illinois on Decem- 
ber 8, 1903. It is the purpose of the Station to conduct inves- 
tigations and make studies of importance to the engineering, 
manufacturing, railway, mining, and other industrial interests of the 
State. 

The management of the Engineering Experiment Station is vested 
in an Executive Staff composed of the Director and his Assistant, the 
Heads of the several Departments in the College of Engineering, and 
the Professor of Industrial Chemistry. This Staff is responsible for 
the establishment of general policies governing the work of the Station, 
including the approval of material for publication. All members of 
the teaching staff of the College are encouraged to engage in scientific 
research, either directly or in cooperation with the Kesearch Corps 
composed of full-time research assistants, research graduate assistants, 
and special investigators. 

To render the results of its scientific investigations available to 
the public, the Engineering Experiment Station publishes and distrib- 
utes a series of bulletins. Occasionally it publishes circulars of timely 
interest, presenting information of importance, compiled from various 
sources which may not readily be accessible to the clientele of the 
Station. 

The volume and number at the top of the front cover page are 
merely arbitrary numbers and refer to the general publications of the 
University. Either above the title or oelow th& seal is given the 
number of the Engineering Experiment Station bulletin or circular 
which should be used in referring to these publications. 

For copies of bulletins or circulars or for other information 
address 

The Engineering Experiment Station, 
University of Illinois, 

Urbana, Illinois. 



UNIVERSITY OF ILLINOIS 
ENGINEERING EXPERIMENT STATION 

Bulletin No. 122 April, 1921 



THE THERMAL CONDUCTIVITY AND 
DIFFUSIVITY OF CONCRETE 



BY 

£. P. CARMAN 
Professor of Physics 

AND 

R. A. NELSON 

Assistant in Physics 



ENGINEERING EXPERIMENT STATION 

Published by the University of Illinois, Urbana 



< 



\H 



2><\ 







^ 



CONTENTS 

PAdfi 

I. Introduction ■ 5 

1. Object of the Investigation ....... 5 

2. Acknowledgments 6 

II. Principles and Methods of Measurement 7 

3. Definitions and Units 7 

4. Method of Measuring Conductivity 9 

5. Method of Measuring Diffusivity 11 

III. Composition and Preparation of the Concrete Cylinders 12 

6. Materials and Proportions Used 12 

IV. Testing Procedure ... 14 

7. Description of Test Specimens and Apparatus 

Used 14 

8. Testing Procedure 16 

9. Tests on a Marble Cylinder 16 

V. Results of Observations and Determinations .... 22 

10. Explanation of Tables 22 

VI. Summary of Results and Conclusions 29 

11. Summary of Results 29 

12. General Conclusions 30 



LIST OF TABLES 

NO. PAGE 

1. Sieve Analysis of Sand and Gravel Used in Concrete Cylinders Tested . 13 

2. Composition of Concrete Mixtures Used in Cylinders Tested .... 13 

3. Properties of Marble 21 

4. Thermal Conductivity of Neat Cement 23 

5. Thermal Conductivity of Concrete, Mixture 1:2 23 

6. Thermal Conductivity of Concrete, Mixture 1:3 24 

7. Thermal Conductivity of Concrete, Mixture 1:4 25 

8. Thermal Conductivity of Concrete, Mixture 1:5 ........ 26 

9. Thermal Conductivity of Concrete, Mixture 1:7 27 

10. Thermal Conductivity of Concrete, Mixture 1:9 27 

11. Thermal Conductivity of "Alabama White" Marble 28 

12. Diffusivity of Concrete and Marble 28 

13. Average Thermal Conductivities of Different Mixtures of Concrete, and 

of Marble, at Different Temperatures 29 

14. Variation of Conductivity with Eelative Water Content 29 

15. Effect of Age on Conductivity 30 

16. Earlier Determinations of Conductivity of Concrete 31 



LIST OF FIGURES 

NO. PAGE 

1. Sectional and End Views of Test Cylinder, showing Location of Heat- 

ing Coil and Thermocouples 14 

2. Cross-sectional Views of Broken Concrete Cylinders . . . . . .17 

3. Method of Insulating and Centering Hot Junction of Thermocouples . 15 

4. General Arrangement of Apparatus and Electrical Circuits .... 15 

5. General View of Apparatus 18 

6. General View of Broken Test Cylinders 19 



THERMAL CONDUCTIVITY AND DIFFUSIVITY 
OF CONCRETE 



I. Introduction 

1. Object of the Investigation.— The object of this investigation 
was to obtain the absolute thermal conductivity of a number of 
standard concrete mixtures. The diffusivity, or thermometric con- 
ductivity, has also been calculated from the specific heat, the density, 
and the thermal conductivity. The investigation was undertaken in 
response to inquiries for information as to such constants from engi- 
neers, received by the Engineering Experiment Station of the Univer- 
sity of Illinois, but, apart from the need of such constants in present 
engineering problems, the increasingly numerous uses of concrete make 
determination of these physical constants for such a common materia] 
desirable. 

In this investigation, it has been considered important to describe 
in detail the material for which the absolute thermal conductivity has 
been determined. During the last ten years the composition and 
methods of preparation of concrete mixtures have been studied and 
standardized, and the present investigators have had the advantage 
of dealing with concrete mixtures which can be described much more 
definitely than was possible a few years ago. The results of only a 
few determinations of the absolute thermal conductivity of concrete 
are recorded in the literature of the subject,* and to a large extent 
these lack definiteness in regard to the composition and method of 
preparation of the material, so that it is impossible to make more than 
a very general comparison of the results here recorded with those 
previously obtained. 



* Proceedings of National Association of Concrete Users, Vol. VII, article by C. L. 
Norton. 1911. 

"Therma-conductivity of Heat Insulators," W. Nusselt. Engineering, Vol. 87, p. 1. 
Jan. 1909. 

"A Study of the Heat Transmission of Building Materials" by A. C. Willard and L. C. 
Lichty. Univ. of 111. Eng. Exp. Sta. Bui. No. 102, 1917. 

Nusselt gives a single determination for "neat" cement, and he did not set a high 
value on this determination. The results of Norton and of Willard and Lichty will be noticed 
later in this bulletin. 



6 ILLINOIS ENGINEERING EXPERIMENT STATION 

Iii addition to determinations of the thermal conductivity of 
concrete, similar determinations for white marble were also made. 
The method used in the determinations for marble was the same as 
had been used for concrete. This not only gives an independently 
determined value of this constant for marble, but also links the de- 
terminations of thermal conductivity for concrete with those for a 
substance for which a number of values of the thermal conductivity 
are given in the literature on the subject.* 

2. Acknowledgments. — In the preparation of the concrete speci- 
mens, we have received valuable help from the Department of Theo- 
retical and Applied Mechanics of the University of Illinois. Professor 
A. N. Talbot, head of the department, has kindly advised with reference 
to descriptive terms for the material tested. To Mr. H. F. Goimerman, 
formerly of the same department, thanks are due for advice and aid 
in the preparation of the large number of concrete cylinders. Mr. 
C. C. Schmidt, Assistant in Physics, aided Mr. Nelson, during the 
summer of 1920, in the preparation of the concrete cylinders and in 
the experimental work. 



* The most extended series of determinations for marble are those of Professor B. O. 
Pierce and Mr. R. W. Wilson, published in the Proceedings of the American Academy of 
Arts and Sciences, Vol. 34, p. 3, 1898. They used a wall method, while the method used 
here was, as will be described, a cylinder method. 



THE THERMAL CONDUCTIVITY AND DIFFUSIVITY OF CONCRETE 



II. Principles and Methods of Measurement 

3. Definitions and Units. — The fundamental fact of heat con- 
ductivity is that, for steady flow, the quantity of heat flowing in a unit 
of time through a plate varies directly as the difference of temperature 
between the faces of the plate, directly as the cross section of the plate, 
and inversely as the thickness of the plate. This law, which was first 
stated clearly by Joseph Fourier, the famous French military engineer 
and mathematician, is expressed by the formula 

Q = k^ST 

In this equation, Q is the quantity of heat, t 2 -t 1 the difference of 
temperature at the two faces, 8 the area of the cross section, T the 
time of flow, and I the distance of flow, or the thickness. The quan- 
tity A: is a constant, which is a property of the material of which the 
body is composed, and is called the thermal conductivity of the ma- 
terial. The fraction — — — - — is the fall of temperature per unit 

i 

distance, and is called the temperature gradient. 

The unit of thermal conductivity clearly depends upon the chosen 
units of length, area, time, and heat. In the following calculations a 
unit based on the centimeter, second, and gram-calorie, called here 
"the c.g.s. physical unit," has been used; but the results are stated 
also in a unit based on the foot, hour, and British thermal unit, called 
here "the British engineering unit." These units are defined as 
follows : 

(a) The C. G. 8. Physical Unit of thermal conductivity corre- 
sponds to the flow of one gram-calorie in one second, when the flow is 
steady, through a section of a plate of the substance in question one 
square centimeter in area, the thickness of the plate being one centi- 
meter, and the difference between the temperatures of the faces of the 
plate one degree centigrade. 

(b) The British Engineering Unit of thermal conductivity cor- 
responds to the flow of one British thermal unit (B.t.u.) in one hour, 
when the flow is steady, through a section of a plate of the substance 
in question one square foot in area, the thickness of the plate being 
one foot, and the difference between the temperatures of the faces of 
the plate one degree Fahrenheit. 



8 ILLINOIS ENGINEERING EXPERIMENT STATION 

The conversion (of results given in either of the above units into 
other units is a matter of simple calculation. 

Upon this subject of units of thermal conductivity the following 
quotation is made from the excellent text-book of Ingersoll and Zoebel 
entitled "The Mathematical Theory of Heat Conduction": "There 
is probably no subject in which the confusion of units is greater than 
that of heat conduction. While the physicist uses the metric or c.g.s. 
unit — that is, the gram-calorie per second, per square centimeter of 
area, for a temperature gradient of a degree centigrade per centimeter 
— there is no such uniformity of practice among engineers. The steam 
engineer refers his observations to the B.t.u. per hour, per square 
foot, per degree Fahrenheit, per inch in thickness, while the refrig- 
erating engineer prefers the day as the unit of time rather than 
the hour, and the electrical engineer uses various systems, based fre- 
quently on the kilowatt, as representing the rate of heat flow. There 
are also numbers of other units, some of them making use of the idea 
of thermal resistance, analogous to electrical resistance, and therefore 
being reciprocally related to conductivity. These various engineering 
units have been introduced to simplify the computation of heat losses 
in various types of problems, and on these grounds perhaps justif}' 
their existence ; but from the standpoint of the present work they are, 
with one or two exceptions, not usable. This is because, in a large 
majority of the cases we shall have occasion to consider, it is not the 
conductivity but the diffusivity, or thermometric conductivity, which 
enters directly into the computations, and this latter is too complex 
a unit to use profitably with a mixture of English and metric systems, 
or an English system involving two different units of length — for 
example, feet and inches, as in common engineering practice. Only 
two, then, of the many heat-conduction units lend themselves readily 
to our purpose — the B.t.u. per hour, per square foot, for a temperature 
gradient of a degree Fahrenheit per foot, and the metric unit. But 
the former is practically never used (the gradient being expressed in 
degrees per inch in the common engineering unit), while the latter is 
becoming of more general use every day, so we shall confine our units 
and calculations to the metric system, giving in many cases, however, 
the English equivalents. ' ■ 

Thermal conductivity expressed in the units defined above, applies 
to the condition of steady flow, that is, the condition existing when the 
temperature at each point through the plate is not changing, and the 



THE THERMAL CONDUCTIVITY AND DIFFUSIVITY OF CONCRETE 9 

quantity of heat entering at one face is equal to the quantity emitted 
at the opposite face. 

There is another constant, which is particularly important to the 
concrete engineer — namely, that which expresses the rate of flow of 
temperature for a material, or the thermal diffusivity. This evidently 
depends not only on the thermal conductivity, but also on the amount 
of heat required to raise the temperature of unit volume of the ma- 
terial one degree : that is, upon the density and the specific heat of 
the material. Thus, if D is the diffusivity, p the density, s the specific 
heat, and k the thermal conductivity of the material, 

d- A 

ps 

In this investigation the thermal diffusivity has been calculated for 
the mixtures for which the thermal conductivity was determined, and 
also for the marble. 

4. Method of Measuring Conductivity. — It is evident that the 
quantities required for the determination of thermal conductivity are 
Q, the quantity of heat passing under steady flow conditions at right 
angles through a surface of predetermined area 8, and the quantity 

2 , 1 i or temperature gradient. For poor heat conductors, such as 

concrete and marble, the method most commonly employed for the 
measurement of the quantities has been the "plate" or "wall" method. 
In this method an essential condition is to have steady flow through 
a flat plate of uniform thickness, and the lines of flow at right angles 
to the faces of the plate ; this condition is practically realized for the 
middle part of an extended disk. The heat may be generated electri- 
cally in a flat coil, and the quantity of heat can be easily calculated 
from the electrical energy consumed. Another method of obtaining 
the quantity of heat Q is to absorb the transmitted heat in a water 
jacket, and measure the rise in temperature of the water. Still another 
method is that used by Lees and Charlton* in which the transmitted 
heat was radiated from a standard plate under constant conditions, the 
constants for this radiated heat having been determined by a separate 
experiment. The method of determining thermal conductivity which 



* Phil. Mag. No. 5, Vol. 41, p. 495, June, 1898, 



10 ILLINOIS ENGINEERING EXPERIMENT STATION 

has been used in this investigation can be described as the "cylinder 
method. " It is the same general method as was used in the determina- 
tion of the thermal conductivity of fire-clay made in this laboratory in 
1909.* A long cylinder of the substance is used, and the heat is 
generated electrically in a coil placed in a hole running axially througli 
the cylinder. Near the ends of the cylinder the flow of heat is, of 
course, not radial, but for some length near the middle of a long 
cylinder we can assume radial flow. Experiments show that this 
assumption is justified. The amount of heat generated per unit length 
of the middle part of the cjdinder is easily calculated from measure- 
ments of the electromotive force, E, and the current, I, flowing in the 
coil. 

To measure the temperature gradient of the heat flow, small 
"probing" holes are placed in the cylinder, parallel to the axis, and 
extending from one end to the middle of the cylinder where the tem- 
perature is to be measured. In most of the cylinders used, there were 
three such holes, one near the coil hole along the axis, one near the 
outer surface of the cylinder, and one about half way between. The 
temperatures can be read by thermocouples placed in these holes. 
Then, knowing the radial distances r x and r 2 , and the corresponding 
temperatures t 1 and t 2 , the temperature gradient is determined directly. 
Fig. 1 shows the arrangement and location of the coil and the thermo- 
couples. 

Fourier 's equation for the stationary flow of heat becomes, in the 
case of a long cylinder, with source along the axis, 

Q = * E kl (t x -t 2 ) T + 
log r 2 /r x 

The equation for the thermal conductivity then becomes 

a. 7 I*. 

* ~ 2 7T I 0HJ T iog r x 

All the quantities on the right-hand side of this equation can be 
directly measured, and thus the absolute thermal conductivity can 
be determined. 



* Thermal Conductivity of Fire Clay at High Temperatures." Univ. of 111. Eng. Exp. 
Sta, Bui. No. 36, 1909. 

t Ingersoll and Zoebel, "The Mathematical Theory of Heat Conduction," p. 27. 



THE THERMAL CONDUCTIVITY AND DIFFUSIVITY OF CONCRETE 11 

5. Method of Measuring Diffusivity. — Diffusivity has already 
been defined as thermal conductivity divided by the product of specific 
heat and density. To determine the diffusivity of a material it is, 
therefore, necessary to determine the specific heat and the density as 
well as the conductivity. 

In the present investigation the ' ' method of mixture ' ' with water 
was used to determine the specific heat. The concrete was broken into 
pieces containing from iy 2 to 2 cubic inches and about 300 grams of 
these pieces were used in each determination. These were heated to 
about 100 deg. C. for four hours in an oven to be sure that all portions 
were at a uniform temperature. 

To determine the specific gravity large pieces of the dried concrete 
were covered with a thin coating of paraffin, and weighed in air, and 
in water. 



12 ILLINOIS ENGINEERING EXPERIMENT STATION 



III. Composition and Preparation of the Concrete Cylinders 

6. Materials and Proportions Used. — In making the concrete 
test cylinders, "Universal" portland cement was used. The sand and 
gravel were of dolomitic limestone from a pit at Attica, Indiana. The 
specific gravity of the stone was about 2.65. The gravel weighed 99 
pounds per cubic foot, loose, and the sand 110 pounds per cubic foot. 
Sieve analyses were made of the sand and gravel, using * ' Tyler stand- 
ard series." The results of the analyses are shown in Table 1. The 
sand was coarse and well suited for making concrete, and the gravel 
was well graded. 

After consideration of various mixtures of sand and gravel, the 
proportion of 55 per cent sand to 45 per cent gravel, by weight, was 
chosen, though the proportioning was actually done by loose volumes. 
These proportions lie between the coarser mixtures that are frequently 
used and the mixtures that have larger percentages of sand ; they gave 
an easily worked mixture. The aggregate of this mixture had a weight 
of 125 lbs. per cubic foot, and this corresponds to 25 per cent of voids. 

Three consistencies were used in the concrete mixtures, the normal 
consistency, which will be referred to as 100 per cent water content, 
and two others, with 10 per cent and 20 per cent additional water, 
respectively, which will be referred to as 110 per cent and 120 per cent 
water content. The normal consistency was such that freshly molded 
concrete in the form of a cylinder 8 inches in diameter by 12 inches 
long, with a 1 :4 mix, would slump y 2 inch to 1 inch when the form 
was removed. 

In Table 2 will be found the proportions of the different constitu- 
ents for the mixtures tested : these proportions are stated on a volume 
basis. In the table the quantity of each constituent in one cubic foot 
of the mixed concrete is also given. 

The forms were removed from the cylinders after the concrete 
had set 24 hours. The cylinders were then stored in damp sand for 
two weeks, and afterwards removed to a dry room. They were all 
thoroughly dry when tested. The appearance of the cross sections of 
broken concrete cylinders is shown in Fig. 2. 



THE THERMAL CONDUCTIVITY AND DIFFUSIVITY OF CONCRETE 



13 



Table 1 

Sieve Analysis of Sand and Gravel Used in Concrete Cylinders Tested 

(Percentages are based upon weight) 





Size of 


Per Cent of Sample Coarser 




Square Opening 


than a Given Sieve 


Sieve Size 








In. 


Mm. 


Sand 


Gravel 


100 mesh 


0.0058 


0.147 


99.0 


100.0 


48 mesh 


0.0116 


0.295 


97.1 


100.0 


28 mesh 


0.0232 


0.59 


81.6 


100.0 


14 mesh 


0.046 


1.17 


52.0 


100.0 


8 mesh 


0.093 


2.36 


33.6 


100.0 


4 mesh 


0.185 


4.70 


8.6 


99.4 


V 8 in. 


0.37 


9.4 


0.0 


97.2 


H in. 


0.75 


18.8 


0.0 


49.8 


1.5 in. 


1.5 


38.1 


0.0 


0.0 



Table 2 

Composition of Concrete Mixtures Used in Cylinders Tested 



Mixture 


Ratios 

Cement: 

Sand: 


Relative 

Water 

Content 

Per Cent 


Volumes in Cu. Ft. 


Cement: 
Aggregate 


Cement 


Sand 


Gravel 


Water 








Cu. Ft. 


Cu. Ft. 


Cu. Ft. 


Cu. Ft. 


1:2 


1-1.2-1.1 


100 
110 
120 


0.50 


0.620 


0.567 


0.282 
0.310 
0.338 


1:3 


1-1.9-1.7 


100 
110 
120 


0.33 


0.62 


0.567 


. 225 
0.248 
0.270 


1:4 


1-2.4-2.3 


100 
110 
120 


0.25 


0.62 


0.567 


0.196 
0.216 
0.235 


1:5 


1-3.1-3.0 


100 
110 
120 


0.20 


0.62 


0.567 


0.176 
0.194 
0.211 


1:7 


1-4.3-4.0 


110 
120 


0.143 


0.62 


0.567 


0.171 
0.186 


1:9 


1-5.6-5.1 


110 
120 


0.111 


0.62 


0.567 


0.160 
0.175 


"Neat" 




100 
110 


1.00 






0.384 
0.423 



14 



ILLINOIS ENGINEERING EXPERIMENT STATION 



IV. Testing Procedure 

7. Description of Test Specimens and Apparatus Used. — The 
cylinders were 24 inches long and iy 2 inches in diameter. The central 
hole for the heating coil was iy 2 inches in diameter. The holes for 
inserting the thermocouples were made by placing 5/32-inch rods in 
the fresh concrete parallel to the axis, and at different radial distances. 
A section of the cylinder and the heating coil is shown in Fig. 1. 



-Thermo -coup/e Ho/es 



Heaf/ng Co/7-y 



K'JS§HSi£SS 




Fig. 1. Sectional and End Views of Test Cylinder, Showing Location of 
Heating Coil and Thermocouples 



The heating coils were made by winding "Chromel C"* ribbon 
0.25 inch by 0.025 inch on hard porcelain insulator tubes 24 inches 
long. In order to center the heating coils, tapered collars for the ends 
were made of portland cement and plaster of Paris. The outer sur- 
faces of the concrete cylinders were covered with a very thin coat of 
plaster of Paris to make the emissivity uniform over the surface of the 
cylinder. The current for the heating coil was supplied by a motor- 
generator set equipped with a General Electric special voltage reg- 
ulator, the motor of the set being driven by the alternating current 
from the University mains, which is of fairly constant voltage. The 
regulator kept the voltage of the 110 D.C. generator constant to within 
less than one-half of one per cent. It was found necessary to heat the 
cylinders from 14 to 16 hours before the temperature became constant 
so that observations could be taken. A Thwing thermocouple recorder 



* This is a nickel-chromium alloy resistance metal made by the Hoskins Manufacturing 
Company of Detroit, Michigan. 



THE THERMAL. CONDUCTIVITY AND DIFFUS1VITY OF CONCRETE 



15 



was used to indicate when a steady condition of temperature was 
reached. 

Fig. 3 shows the method of insulating the hot junction of the 
thermocouple and centering it in the hole ; the outside glass protecting 
tube fitted closely in the holes in the cylinder. Copper-constantan 
thermocouples were used, and were calibrated by first of all determining 
the readings at three fixed temperatures, the boiling point of water, 



Th&rmo-coup/e Junct/on 



:> 



I 



/nsu/c?Nng Tube-g/a&s—^ Protect/ng Jacket- g/ass 

Fig. 3. Method of Insulating and Centering Hot Junction of 
Thermocouples 



the boiling point of napthalene, and the melting point of lead. These 
three points having been determined, the complete calibration curve for 
each couple was drawn by comparison with the calibration curve for a 
standard thermocouple, that had been carefully calibrated. A Wolff 
potentiometer was used to measure the electromotive force. The gen- 
eral arrangement of the apparatus and circuits are'shown in Figs. -1 
and 5. 




Fig. 4. General Arrangement of Apparatus and Electrical Circuits 



16 ILLINOIS ENGINEERING EXPERIMENT STATION 

8. Testing Procedure. — Temperature readings were taken for 
most of the cylinders at three radial distances from the axis. On the 
first tests a thermocouple was used in each hole and temperatures were 
taken simultaneously, but it was afterwards found that one thermo 
couple could be used, and changed from one hole to the other, without 
affecting the accuracy of the observations. Temperature readings 
were taken over a range of five centimeters axial length at the middle 
of the cylinder. Preliminary tests had shown that for this portion 
of the cylinder there was practically no variation in temperature 
parallel to the axis ; that is, the flow of heat was truly radial through 
this mid-portion of the cylinder. The current through the heating 
coils and the potential differences were read at the beginning and at 
the end of each set of observations. In most of the determinations a 
length of heating coil of 59 cm. was used, but for a few cases the 
length was 57.5 cm. Before taking any test temperature readings the 
cylinders were first given a preliminary heating to a temperature of 
over 100 deg. C. in order to dry them out ; this was found to be neces- 
sary in order to obtain consistent readings. 

After the tests were completed the cylinders were broken as near 
the middle as possible and the radial distances of the thermocouple 
holes from the cylinder axes were measured. In calculating the 
thermal conductivity, these measured radial distances were used, with 
the corresponding temperatures. 

Fig. 2 shows sectional views of the cylinders when broken, and 
the probing holes for measuring the temperature can be seen. Fig. 6 
shows a collection of cylinders which were tested. Kesults of experi- 
ments on fifty-one concrete cylinders are given in the tables. 

9. Tests on a Marble Cylinder. — In addition to the tests on the 
concrete cylinders, some tests were made on a cylinder of marble, of 
similar dimensions. White Alabama marble was used, the sample 
having been purchased from the Peoria Marble Works of Peoria, 
Illinois. The grain of this marble was of a fine sugary texture and the 
specimen is described as being of a "very good grade" of marble. 
Chemical analysis showed that it was composed principally of calcium 
carbonate, with a small amount of magnesium carbonate. The tests 
were made both for thermal conductivity and for diffusivity. Before 
testing, in order to free the marble from moisture, it was heated to 
130 deg. C. in a large oven for four hours. In carrying out the con- 





/-2 Mixture 



i-3 Mixture 




■f^. 


'Zr** 


l r "^ 




. ^.V'fj^ 


d&k 


1 - JW 




,' « I! 




%0&? 




■■; , * jf 


■ 


" y » ^ 


W# 


- j'^^d 


^j.-.i 


i# ^^^ 





i-4 Mixture 



t-S Mixture 



W^K. 





/ -7 Mixture 




/-9 Mixture 



Fig. 2. Cross-sectional Views of Broken Concrete Cylinders 




Fig. 5. General View of Apparatus 




Fig. 6. General View of Broken Test Cylinders 



THE THKK.MAL CONDUCTIVITY AND DIFFUSIVITY OF CONCRETE 



21 



ductivity tests tlio cylinder was first heated to about 50 deg. C. and 
readings taken; the temperature was then increased each day, and 
observations made, until a temperature of about 200 deg. C. was 
readied ; the specimen was then allowed to cool, and was again tested 
in the same manner. At about 235 deg. C. the cylinder cracked in 
several places, and observations were discontinued. The results of 
the conductivity tests are given in Table 11 ; the mean values for the 
conductivity are given in Table 13. 

For purposes of comparison, in Table 3 are given figures for 
specific gravity, specific heat, thermal conductivity, and diffusivity 
for the sample tested, and also for another sample of a somewhat 
similar marble, the values given in the latter case having been taken 
from results already published by Pierce and Wilson.* 

Table 3 
Properties of Marble 





Pierce and Wilson's 
"American White" 


"Alabama White" 


Specific gravity 


2.72 
0.214 
0.00596 
0.0102 


2.71 


Specific heat 


0.213 


Thermal conductivity 


0.00614 


Diffusivity . . .• 


0.0106 







* Proc. Am. Acad. Arts and Sciences, Vol. 36, 1900. 



22 ILLINOIS ENGINEERING EXPERIMENT STATION 



V. Kesults of Observations and Determinations 

10. Explanation of Tables. — The results of the observations and 
calculations are shown in Tables 4 to 11. Tests were made on fifty-one 
concrete cylinders, including three cylinders of "neat" cement, and 
on one cylinder of "White Alabama" marble. The first column gives 
the identification mark for the cylinder ; the second column gives the 
"relative water content" as defined in Section III, page 12; the third 
column gives the number of days, at the time of test, since the cylinder 
was cast ; the fourth and fifth columns give the radial distances r t and 
r 2 of the probing holes at which the temperatures t 1 and t 2 , given in the 
eighth and ninth columns, were measured; the sixth and seventh 
columns give respectively the current / in amperes, and the electro- 
motive force E in volts of the heating coil, for calculating the heat Q ; 
the tenth and eleventh columns give the values of k, the thermal con- 
ductivity in "c.g.s." and "British engineering" units as defined in 
Section II, page 7; the material of the cylinder is indicated in the 
caption. The proportions of the concrete mixtures are given in Table 2. 

In Table 12 are given values for densities, specific heats, con- 
ductivities, and diffusivities, for the different mixtures of concrete, 
and for the marble. These values for concrete are given for one 
relative water content only, namely, 110 per cent; it was considered 
that thus good average values would be obtained, and that in any case 
the diffusivity would not show much variation with variation of the 
relative water content. 

In calculating the diffusivities the conductivities determined for 
a range of temperature of from 100 deg. C. to 200 deg. C. were used. 
This was done because it was felt that these results were more reliable, 
both on account of the larger number of readings taken over this range, 
and because the readings were somewhat more consistent, owing to the 
larger temperature differences. 



THE THERMAL CONDUCTIVITY AM) DIFFUSIVITY OF CONCRETE 



23 



Table 4 
Thermal Conductivity of Neat Cement 





Relative 
















k 


k 


Cylinder 


Water 


Age 


ri 


r 2 


I 


E 


ti 


t 2 


c. g. s. 


British 


Mark 


Content 

Per Cent 




cm. 


cm. 


Amp. 


Volts 


deg. C. 


deg. C. 


Physical 


Engi- 
neering 


1H 


100 


28 


3.493 


6.055 


15.67 


27 . 30 


253.7 


152.5 


0.00150 


0.363 








3.493 


9.508 






253.7 


91.5 


0.00170 


0.411 


1H 


100 


120 


3.493 


6 . 055 


17.02 


29.7 


345.7 


212.1 


0.00135 


0.327 








6.055 


9.508 






212.1 


123.0 


0.00165 


0.399 








3.493 


9.50S 






345.7 


123.0 


0.00147 


. 356 


1H 


100 


150 


3.493 


6 . 055 


7.48 


12.15 


91.0 


67.6 


0.00138 


0.334 








(5.055 


9 . 50S 






67.6 


49.0 


0.00142 


0.344 








3.493 


9 . 50S 






91.0 


49.0 


0.00140 


0.339 


3H 


110 


28 


2.244 


4.95S 


13.99 


24.40 


286.6 


148.8 


0.00126 


0.305 








2.244 


8.799 






286.6 


89.2 


0.00153 


0.370 


4H 


110 


28 


2.990 


6.378 


13.99 


25.00 


217.1 


112.9 


0.00164 


0.397 



Table 5 

Thermal Conductivity of Concrete 

Mixture 1:2 



Cylinder 
Mark 



Relative 
Water Age 
Content Days 
Per Cent 



cm. 



r 2 

cm. 



I 
Amp. 



E 
Volts 



ti 
deg. C. 



t 2 
deg. C. 



k 

c. g. s. 

Physical 



k 
British 
Engi- 
neering 



IE 



IE 
2E 



2E 
2E 



3E 

3E 
3E 
3E 
4E 



5E 
5E 



6E 



6E 

7E 



110 


28 


2.394 


4.811 






2.394 


8.662 


110 


120 


2.394 


4.811 


110 


28 


2.161 


6.131 






6.131 


9 . 255 






2.161 


9.255 


110 


120 


2.161 


6.131 


110 


140 


2.161 


6.131 






6.131 


9.255 






2.161 


9.255 


100 


28 


2.313 


7.390 






2.313 


7.567 






2.313 


7.390 






2.313 


7.567 


100 


120 


2.313 


7.390 






2.313 


7.567 


100 


140 


2.313 


7.390 






2.313 


7.567 


100 


150 


2.313 


7.390 






2.313 


7.567 


120 


28 


4.860 


6.372 






6 . 372 


9.270 






4.860 


9.270 


110 


28 


3.978 


9.297 


110 


120 


4.423 


9.297 






3.978 


9.297 


100 


28 


2.528 


7 . 105 






2.528 


7.936 






2.528 


7.105 






2.528 


7.936 


100 


120 


2.528 


7.105 






2.528 


7.936 


100 


28 


3.003 


5.493 






3.003 


9.123 



16.41 



19.00 
16.37 



19.00 
7.52 



15.64 
16.18 
17.02 
7.55 
19.13 
16.18 

16.36 
15.08 

16.79 

16.79 

15.09 

16.18 



26.10 



32.95 
28.40 



33.35 
12.21 



24.80 
25.25 
29.70 
12.39 
32.80 
28.00 

26.00 
25.61 

27.80 

28.30 

26.35 

28.25 



197.2 
197.2 
321.8 
239.3 
145.3 
239.3 
354.2 
76.4 
56.3 
76.4 
194.2 
194.2 
221.0 
221.0 
265.4 
265 . 4 
68.7 
68.7 
334.7 
334.7 
170.4 
137.4 
170.4 
174.7 
155. S 
170.1 
245.2 
245.2 
260.0 
260.0 
220.9 
220.9 
189.4 
189.4 



\t 



138.8 
103.4 
229.4 
145.3 
104.9 
104.9 
210.8 
56.3 
48.0 
48.0 
115.6 
113.9 
132.5 
128.2 
151.1 
142.4 
49.5 
48.9 
175.4 
174.3 
137.4 
110.2 
110.2 
105.2 
107.8 
107.8 
151.4 
134.1 
161.4 
143.1 
140.5 
121.8 
144.7 
112.9 



0.0033 
0.0038 
0.0031 
. 0033 
0.0031 
0.0033 
0.0031 
0.0031 
0.0029 
0.0030 
0.0037 
0.0037 
0.0035 
0.0034 
0.0034 
0.0032 
0.0037 
0.0036 
0.0030 
0.0031 
0.0024 
0.0040 
0.0031 
0.0033 
0.0038 
0.0034 
0.0033 
0.0031 
0.0035 
0.0030 
0.0034 
0.0030 
0.0040 
0.0043 



0.80 
0.92 
0.75 
0.80 
0.75 
0.80 
0.75 
0.75 
0.70 
0.73 
0.90 
0.90 
0.85 
0.82 
0.82 
0.77 
0.90 
0.87 
0.73 
0.75 
0.58 
0.97 
0.75 
0.80 
0.92 
0.82 
0.80 
0.75 
0.85 
0.73 
0.82 
0.73 
0.97 
1.04 



24 



ILLINOIS ENGINEERING EXPERIMENT STATION 











Table 6 














Thermal Conductivity of Concrete 












Mixture 1:3 








Relative 
















k 

c. g. s. 

Physical 


k 


Cylinder 

Mark 


Water 
Content 
Per Cent 


Age 
Days 


ri 

cm. 


r 2 

cm. 


I 
Amp. 


E 
Volts 


ti 
deg. C. 


t 2 
deg. C. 


British 
Engi- 
neering 


ID 


110 


28 


2.594 


6.776 


15.80 


24.85 


175.4 


115.1 


0.0040 


0.97 








2.594 


6.776 


19.72 


30.35 


289.6 


171.5 


0.0031 


0.75 








6.776 


9.196 






171.5 


132.5 


0.0030 


0.73 








2.594 


9.196. 






289.6 


132.5 


0.0031 


0.75 


2D 


100 


28 


2.467 


4.904 


15.80 


27.50 


196.2 


138.7 


0.0034 


0.82 








2.467 


8.713 






196.2 


104.1 


0.0038 


0.92 








2.467 


4.904 


19.75 


34.55 


312.5 


217.3 


0.0032 


0.77 








4.904 


8.713 






217.3 


155.2 


0.0041 


0.99 








2.461 


8.713 






312.5 


155.2 


0.0035 


0.85 


3D 


110 


28 


2.420 


7.097 


15.09 


23 . 45 


159.1 


107.5 


0.0048 


1.16 








2.420 


7.097 


16.00 


26.00 


199.8 


133.0 


0.0044 


1.06 








2.420 


9.024 






199.8 


105.7 


0.0038 


0.92 


4D 


110 


28 


2.220 


8.841 


15.10 


26.15 


185.2 


98.2 


0.0040 


0.97 








2.220 


4.197 


16.00 


27.50 


222.9 


168.9 


0.0034 


0.82 








4.197 


8.841 






168.9 


116.1 


0.0040 


0.97 








2.220 


8.841 






222.9 


116.1 


0.0037 


0.90 


5D 


110 


28 


2.307 


5.852 


17.12 


29.75 


234.7 


164.8 


0.0044 


1.06 








5.852 


9.235 






164.8 


126.2 


. 0039 


0.94 








2.307 


9.235 






234.7 


126.2 


0.0042 


1.01 


5D 


110 


120 


2.307 


5.852 


14.94 


24.00 


181.7 


121.7 


0.0036 


0.87 








5.852 


9.235 






121.7 


94.0 


0.0038 


0.92 








2.307 


9.235 






181.7 


94.0 


0.0037 


0.90 


5D 


110 


140 


2.307 


5.852 


7.46 


12.02 


72.0 


54.0 


0.0031 


0.75 








5.852 


9.235 






54.0 


47.0 


0.0039 


0.94 








2.307 


9.235 






72.0 


47.0 


0.0033 


0.80 


6D 


110 


28 


4.478 


9.252 


17.14 


26.55 


168.4 


120.5 


0.0044 


1.06 








2.474 


9.252 






228.1 


120.5 


0.0036 


0.87 


6D 


110 


120 


2.474 


4.478 


14.94 


24.40 


169.5 


135.9 


0.0043 


1.04 


7D 


120 


28 


2.535 


6.225 


16.43 


28.45 


226.5 


147.1 


0.0034 


0.82 








6.225 


9.255 






147.1 


118.6 


0.0037 


0.90 








2.535 


9.255 






226.5 


118.6 


0.0036 


0.87 


7D 


120 


120 


2.535 


6.225 


13.83 


24.00 


179.3 


121.1 


0.0033 


0.80 








6.225 


9.255 






121.1 


95.1 


0.0035 


0.85 








2.535 


9.255 






179.3 


95.1 


0.0033 


0.80 


7D 


120 


140 


2.535 


6.225 


7.51 


12.25 


70.8 


54.5 


0.0033 


0.80 








6.225 


9.255 






54.5 


46.6 


0.0032 


0.77 








2.535 


9.255 






70.8 


46.6 


0.0032 


0.77 


8D 


100 


28 


2.253 


4.953 


16.17 


25.60 


188.8 


138.9 


0.0042 


1.01 








4.953 


7.819 






138.9 


110.1 


0.0042 


1.01 








2.253 


7.819 






188.8 


110.1 


0.0042 


1.01 


9D 


100 


28 


2.360 


4.230 


16.77 


28.80 


248.9 


194.8 


0.0034 


0.82 








4.230 


9.131 






194.8 


127.7 


. 0036 


0.87 








2.360 


9.131 






248.9 


127.7 


0.0036 


0.87 








2.360 


4.230 


16.79 


29.10 


259.8 


200.1 


0.0031 


0.75 








4.230 


9.131 






200.1 


132.2 


0.0038 


0.92 








2.360 


9.131 






259.8 


132.2 


0.0033 


0.80 


9D 


100 


120 


2.360 


4.230 


13.83 


24.65 


183.8 


145.0 


0.0034 


0.82 








4.230 


9.131 






145.0 


103.6 


0.0042 


1.01 








2.360 


9.131 






183.8 


103.6 


0.0038 


0.92 


9D 


100 


140 


2.360 


4.230 


7.73 


12.50 


71.9 


60.5 


0.0033 


0.80 








4.230 


9.131 






60.5 


46.9 


0.0036 


0.87 








2.360 


9.131 






71.9 


46.9 


0.0035 


0.85 


11D 


120 


120 


2.653 


5.539 


12.88 


21.90 


143.6 


103.5 


0.0033 


0.80 








2.653 


9.073 






143.6 


85.0 


0.0038 


0.92 








2.653 


5.539 


14.56 


25.00 


189.9 


137.0 


0.0033 


0.80 








2.653 


9.073 






189.9 


105.9 


0.0034 


0.82 








2.653 


5.539 


13.83 


23.60 


173.7 


126.5 


0.0033 


0.80 








2.653 


9.073 






173.7 


98.5 


0.0035 


0.85 


11D 


120 


140 


2.653 


5.539 


7.26 


11.77 


66.1 


52.8 


0.0031 


0.75 








2.653 


9.073 






66.1 


46.1 


. 0034 


0.82 








2.653 


9.073 


10.17 


17.10 


106.2 


65.6 


0.0034 


0.82 








2.653 


9.073 


13.96 


23.90 


176.9 


97.5 


0.0033 


0.80 








2.653 


5.539 


18.19 


31.00 


268.0 


181.6 


0.0031 


0.75 








2.653 


9.073 






268.0 


124.4 


0.0031 


0.75 








2.653 


5.539 


18.26 


31.10 


283.5 


195.0 


0.0031 


0.75 








2.653 


9.073 






283.5 


139.6 


0.0031 


0.75 



THE THERMAL CONDUCTIVITY AND DIFFUSIVITY OF CONCRETE 



25 



Table 7 

Thermal Conductivity of Concrete 

Mixture 1 : 4 





Relative 
















k 


k 


Cylinder 


Water 


Age 


Tl 


r 2 


I 


E 


ti 


t 2 


c. g. s. 


British 


Mark 


Content 
Per Cent 


Days 


cm. 


cm. 


Amp. 


Volts 


deg. C. 


deg. C. 


Physical 


Engi- 
neeiing 


1C 


110 


28 


2.616 


5.038 


15.28 


24.05 


161.4 


119.2 


0.0037 


0.90 








5.038 


8.293 






119.2 


94.2 


0.0047 


1.14 








2.616 


8.293 






161.4 


94.2 


0.0041 


0.99 








2.616 


5.038 


19.81 


32.61 


322.5 


240.5 


0.0033 


0.80 








5.038 


8.293 






240.5 


168.8 


0.0029 


0.70 








2.616 


8.293 






322.5 


168.8 


0.0031 


0.75 


2C 


100 


28 


2.498 


4.406 


15.58 


26.75 


176.8 


136.2 


0.0038 


0.92 








4.406 


6.693 






136.2 


111.7 


0.0046 


1.11 








2.498 


6.693 






176.8 


111.7 


0.0041 


0.99 


3C 


110 


28 


2.440 


6.455 


15.61 


24.1 


192.9 


116.9 


0.0031 


0.75 








6.455 


7.395 






116.9 


107.8 


0.0036 


0.87 








2.440 


7.395 






192.9 


107.8 


0.0032 


0.77 


3C 


110 


120 


2.440 


6.455 


15.00 


25.95 


199.6 


133.8 


0.0037 


0.90 








6.455 


7.395 






133.8 


121.4 


0.0028 


0.68 








2.440 


7.395 






199.6 


121.4 


0.0036 


0.87 


3C 


110 


140 


2.440 


6.455 


7.52 


12.21 


65.2 


50.8 


0.0040 


0.97 








2.440 


7.395 






65.2 


50.1 


0.0043 


1.04 


3C 


110 


150 


2.440 


6.455 


19.14 


32.81 


317.3 


196.0 


0.0036 


0.87 


4C 


110 


28 


2.639 


3.679 


16.41 


26.00 


198.3 


177.8 


0.0044 


1.06 








3.679 


9.469 






177.8 


104.1 


0.0035 


0.85 








2.639 


9.464 






198.3 


104.1 


. 0037 


0.90 


5C 


110 


28 


2.700 


5.852 


16.41 


28.50 


207.7 


148.0 


0.0039 


0.94 








2.700 


9.125 






207.7 


122.4 


0.0043 


1.04 


6C 


100 


28 


5.569 


9.103 


15.90 


27.55 


158.5 


122.1 


0.0037 


0.90 


6C 


100 


120 


5.569 


9.103 


14.96 


25.9 


142.4 


108.5 


0.0036 


0.87 








4.588 


9.103 






159.9 


108.5 


0.0033 


0.80 


7C 


100 


28 


2.494 


6.998 


15.84 


27.85 


234.2 


143.2 


0.0032 


0.77 








6.998 


8.725 






143.2 


125.5 


0.0035 


0.85 








2.494 


8.725 






234.2 


125.5 


0.0033 


0.80 


7C 


100 


120 


2.494 


6.998 


14.93 


26.20 


216.2 


128.9 


0.0030 


0.73 








2.494 


8.725 






216.2 


118.5 


0.0032 


0.77 


8C 


120 


28 


2.232 


5.966 


15.21 


26.35 


232.5 


147.8 


0.0030 


0.73 








5. '966 


9.467 






147.8 


114.0 


0.0035 


0.85 








2.232 


9.467 






232.5 


114.0 


0.0032 


0.77 


8C 


120 


120 


2.232 


5.966 


14.93 


26.05 


229.0 


136.8 


. 0028 


0.68 


IOC 


120 


28 


2.563 


5.588 


16.01 


27.35 


238.6 


152.9 


0.0026 


0.63 








5.588 


9.075 






152.9 


113.8 


0.0035 


0.85 








2.563 


9.075 






238.6 


113.8 


0.0029 


0.70 


IOC 


120 


120 


2.563 


5.588 


17.61 


31.15 


273.4 


186.9 


0.0033 


0.80 








5.588 


9.075 






186.9 


133.6 


0.0033 


0.80 








2.563 


9.075 






273.4 


133.6 


0.0033 


0.80 








2.563 


9.075 


14.92 


26.25 


216.2 


118.3 


0.0034 


0.82 


IOC 


120 


140 


2.563 


5.588 


7.53 


12.31 


66.2 


56.8 


0.0051 


1.23 








5.588 


9.075 






56.8 


47.2 


0.0031 


0.75 








2.563 


9.075 






66.2 


47.2 


0.0041 


0.99 



26 



ILLINOIS ENGINEERING EXPERIMENT STATION 



Table 8 

Thermal Conductivity of Concrete 

Mixture 1:5 





Relative 
















k 

c. g. s. 

Physical 


k 


Cylinder 


Water 


Age 


ri 


r 2 


I 


E 


ti 


t 2 


British 


Mark 


Content 
Per Cent 


Days 


cm. 


cm. 


Amp. 


Volts 


cleg. C. 


deg. C. 


Engi- 
neering 


IB 


110 


28 


2.531 


8.890 


72.3 


7.12 


244.7 


128.0 


0.0035 


0.84 


IB 


110 


28 


2.531 


8.890 


90.0 


8.71 


360.1 


176.4 


0.0034 


0.82 


3B 


110 


28 


2.651 


3.298 


12.05 


19.00 


116.0 


105.1 


0.0037 


0.90 








3.298 


7.595 






105.0 


80.8 


0.0041 


0.99 








2.651 


7.595 






116.0 


80.8 


0.0045 


1.09 


4B 


110 


28 


2.610 


6.014 


12.05 


20.95 


101.2 


83.4 


0.0035 


0.85 








2.010 


8.510 






101.2 


71.5 


0.0040 


0.97 


5B 


110 


28 


2.512 


4.666 


11.83 


20.30 


122.2 


96.7 


0.0037 


0.90 








4.666 


8.522 






96.7 


75.3 


0.0035 


0.85 








2.512 


8.522 






122.2 


75.3 


0.0033 


0.80 








2.512 


4.666 


19.80 


29.65 


290.8 


233.6 


0.0041 


0.99 








4.666 


8.522 






233.6 


170.9 


0.0036 


0.87 








2.512 


8.522 






290.8 


170.9 


0.0039 


0.94 








2.512 


4.666 






154.6 


115.8 


0.0041 


0.99 








4.666 


8.522 






115.8 


96.2 


0.0040 


0.97 








2.512 


8.522 






154.6 


96.2 


0.0040 


0.97 


6B 


100 


28 


2.474 


6.064 


16.02 


25.4 


210.7 


146.7 


0.0039 


0.94 








6.064 


9.181 






146.7 


114.5 


0.0034 


0.82 








2.474 


9.181 






210.7 


114.5 


0.0036 


0.87 


6B 


100 


120 


2.474 


6.064 


14.93 


26.10 


211.0 


138.8 


0.0032 


0.77 








6.064 


9.181 






138.8 


110.0 


0.0037 


0.89 








2.474 


9.181 






211.0 


110.0 


0.0034 


0.82 


7B 


120 


28 


2.308 


7.043 


15.08 


26.70 


235.3 


129.6 


0.0028 


0.68 








7.043 


8.550 






129.6 


116.3 


0.0038 


0.92 








2.308 


8.550 






235.3 


116.3 


0.0029 


0.70 


7B 


120 


120 


2.308 


7.043 


14.92 


26.01 


232.9 


126.3 


0.0027 


0.65 








7.043 


8.550 






126.3 


110.6 


0.0031 


0.75 








2.308 


8.550 






232.9 


110.6 


0.0027 


0.65 








2.308 


7.043 


7.73 


12.54 


80.3 


54.8 


0.0028 


0.68 








7.043 


8.550 






54.8 


49.0 


0.0021 


0.51 








2.308 


8.550 






80.3 


49.0 


0.0027 


0.65 


7B 


120 


150 


2.308 


7.043 


19.14 


32.70 


375.5 


188.9 


0.0025 


0.61 








7.043 


8.550 






188.9 


157.7 


0.0025 


0.61 








2.308 


8.550 






375.5 


157.7 


0.0025 


0.61 


8B 


120 


28 


4.788 


5.586 


15.09 


26.40 


163.6 


154.3 


0.0043 


1.04 








5.586 


9.288 






154.3 


114.4 


0.0033 


0.80 








4.788 


9.288 






163.6 


114.4 


0.0034 


0.82 


8B 


120 


120 


4.788 


5.586 


14.94 


25.91 


162.9 


145.7 


0.0025 


0.60 








5.586 


9.288 






145.7 


107.4 


0.0034 


0.80 








4.788 


9.288 






162.9 


107.4 


0.0030 


0.73 


9B 


120 


28 


2.304 


6.754 


15.64 


27.45 


238.5 


136.8 


0.0029 


0.70 








6.754 


9.187 






136.8 


109.0 


0.0031 


0.75 








2.304 


9.187 






238.5 


109.0 


0.0030 


0.73 


9B 


120 


120 


2.304 


6.754 


17.61 


30.61 


293.0 


162.1 


0.0028 


0.68 








6.754 


9.187 






162.1 


133.4 


0.0036 


0.87 








2.304 


9.187 






293.0 


133.4 


0.0030 


0.73 


9B 


120 


140 


2.304 


6.754 


7.73 


12.60 


78.2 


51.7 


0.0026 


0.63 








6.754 


9.187 






51.7 


46.3 


0.0035 


0.85 








2.304 


9.187 






78.2 


46.3 


0.0027 


0.65 



THE THERMAL CONDUCTIVITY AND DIFFUSIVITY OF CONCRETE 



27 



Table 9 

Thermal Conductivity of Concrete 

Mixture 1:7 





Relative 
















k 


k 


Cylinder 


Water 


Age 


ri 


r 2 


I 


E 


ti 


t 2 


c. g. s. 


British 


Mark 


Content 
Per Cent 


Days 


em. 


cm. 


Amp. 


Volts 


deg. C. 


deg. C. 


Physical 


Engi- 
neering 


IF 


110 


2S 


5.224 


7.641 


16.72 


27.15 


167.4 


137.8 


0.0036 


0.87 








3.395 


7.641 






190.1 


137.8 


0.0043 


1.04 


2F 


110 


28 


4.599 


8.178 


16.71 


28.85 


178.4 


128.8 


0.0036 


0.87 


3F 


120 


2S 


2.468 


5.463 


15.76 


24.40 


216.3 


142.0 


0.0027 


0.65 








5.463 


7.058 






142.0 


119.4 


0.0028 


0.68 








2.468 


7. OSS 






216.3 


119.4 


0.0027 


0.65 


3F 


120 


120 


5.463 


7.058 


15.61 


27.10 


152.4 


130.3 


0.0032 


0.77 


4F 


120 


28 


5.724 


8.096 


15.76 


27.10 


148.8 


117.5 


0.0031 


0.75 








3.787 


8.096 






173.7 


117.5 


0.0031 


0.75 


5F 


110 


28 


5.190 


8.772 


15.55 


23.25 


141.9 


114.1 


. 0044 


1.06 








3.050 


8.772 






194.3 


114.1 


0.0031 


0.75 


5F 


110 


120 


3.050 


5.190 


15.62 


27.30 


196.0 


155.0 


0.0037 


0.90 








5.190 


8.772 






155.0 


120.6 


0.0043 


1.04 








3.050 


8.772 






196.0 


120.6 


0.0040 


0.97 


5F 


110 


140 


3.050 


5.190 


7.47 


12 . 15 


65.0 


55.5 


0.0041 


0.99 








5.190 


8.772 






55.5 


48.3 


0.0043 


1.04 








3.050 


8.772 






65.0 


48.3 


3.0037 


0.90 


6F 


120 


28 


2.296 


6.491 


15.70 


27.20 


224.7 


148.7 


0.0037 


0.90 








6.491 


9.174 






148.7 


110.8 


0.0026 


0.63 








2.296 


9.174 






224.7 


110.8 


0.0033 


0.80 



Table 10 

Thermal Conductivity of Concrete 

Mixture 1:9 





Relative 
















k 


k 


Cylinder 


Water 


Age 


Ti 


I"2 


I 


E 


ti 


t 2 


c. g. s. 


British 


Mark 


Content 
Per Cent 


Days 


cm. 


cm. 


Amp. 


Volts 


deg. C. 


deg. C. 


Physical 


Engi- 
neering 


1G 


110 


28 


2.362 


4.828 


16.1 


25.3 


234.0 


155.4 


0.0024 


0.58 


2G 


110 


28 


3.642 


5.232 


16.08 


27.70 


190.7 


161.0 


0.0035 


0.85 








5.232 


7.976 






161.0 


126.6 


0.0035 


0.85 








3.642 


7.976 






190.7 


126.6 


0.0035 


0.85 


2G 


110 


120 


3.642 


5.232 


15.38 


26.30 


172.4 


150.3 


0.0044 


1.06 








5.232 


7.976 






150.3 


119.6 


0.0037 


0.90 








3.642 


7.976 






172.4 


119.6 


0.0040 


0.97 


3G 


110 


28 


3.315 


5.595 


16.00 


24.00 


194.9 


150.8 


. 0030 


0.73 








5 . 595 


7.495 






150.8 


130.1 


0.0035 


0.85 








3.315 


7.495 






194.9 


130.1 


0.0031 


0.75 


3G 


110 


120 


3.315 


7.495 


15.27 


26.65 


174.5 


118.5 


0.0038 


0.92 


3G 


110 


150 


3.315 


5.595 


7.55 


12.44 


58.8 


53.4 


. 0060 


1.45 








5.595 


7.495 






53.4 


50.0 


0.0054 


1.30 








3.315 


7.495 






58.8 


50.0 


0.0058 


1.41 


3G 


110 


150 


3.315 


7:495 


19.13 


32.65 


259.4 


172.5 


0.0038 


0.92 


4G 


110 


28 


4.589 


4.978 


15.97 


26.50 


170.0 


164.2 


0.0038 


0.92 








4.978 


7.611 






164.2 


133.4 


0.0038 


0.92 








4.587 


7.611 






170.0 


133.4 


0.0038 


0.92 


4G 


110 


120 


4.589 


4.978 


15.27 


26.85 


159.9 


154.6 


0.0042 


1.02 








4.978 


7.611 






154.6 


121.7 


0.0035 


0.85 








4.589 


7.611 






159.9 


121.7 


0.0036 


0.87 


5G 


120 


28 


2.316 


5.234 


15.55 


23.20 


228.8 


162.8 


0.0029 


0.70 








5.234 


9.134 






162.8 


112.9 


0.0026 


0.63 








2.316 


9.134 






228.8 


112.9 


0.0027 


0.65 



28 



ILLINOIS ENGINEERING EXPERIMENT STATION 



Table 11 
Thermal Conductivity of ''Alabama White" Marble 



Fl 


r 2 


I 


E 


ti 


t 2 


k 

C. g. 8. 


k 
British 


cm. 


cm. 


Amp. 


Volts 


deg. C. 


deg. C. 


Physical 


Engineering 


2.890 


6.401 


7.25 


11.71 


58.7 


51.5 


0.0063 


1.52 


6.401 


8.911 






51.5 


48.3 


0.0059 


1.43 


2.890 


6.401 


9.53 


16.10 


79.9 


67.4 


0.0065 


1.57 


6.401 


8.911 






67.4 


62.3 


0.0066 


1.60 


2.890 


8.911 






79.9 


62.3 


0.0066 


1.60 


2.890 


6.401 


10.18 


17.20 


88.6 


71.6 


0.0055 


1.33 


6.401 


8.911 






71.6 


65.1 


0.0061 


1.48 


2.890 


8.911 






88.6 


65.1 


0.0056 


1.36 


6.401 


8.911 


12.87 


22.05 


101.6 


91.5 


0.0062 


1.50 


2.890 


6.401 






128.4 


101.6 


0.0055 


1.33 


2.890 


8.911 






128.4 


91.5 


0.0059 


1.43 


2.890 


6.401 


13.83 


23.50 


146.7 


114.0 


0.0053 


1.28 


6.401 


8.911 






114.0 


99.9 


0.0055 


1.33 


2.890 


8.911 






146.7 


99.9 


0.0052 


1.26 


2.890 


6.401 


13.96 


24.00 


147.9 


110.4 


0.0048 


1.16 


6.401 


8.911 






110.4 


96.8 


0.0054 


1.31 


2.890 


8.911 






147.9 


96.8 


0.0049 


1.19 


2.890 


6.401 


14.58 


24.90 


160.3 


124.1 


0.0053 


1.28 


6.401 


8.911 






124.1 


107.9 


0.0050 


1.21 


2.890 


8.911 






160.3 


107.9 


0.0052 


1.26 


6.401 


8.911 


18.19 


31.11 


147.0 


119.4 


0.0045 


1.09 


2.890 


6.401 






219.6 


147.0 


0.0041 


0.99 


2.890 


8.911 






219.6 


119.4 


0.0042 


1.02 


6.401 


8.911 


18.27 


31.25 


160.4 


133.3 


0.0047 


1.14 


2.890 


6.401 






235.2 


160.4 


0.0041 


0.99 


2.890 


8.911 






235.2 


133.3 


0.0042 


1.02 



Table 12 
dlffusivity of concrete and marble 





Relative 

Water 

Content 

Per Cent 


Density 


Conductivity 


Specific Heat 


Diffusivity 


Mixture 


gms. per 
c. c. 


lbs. per 
cu. ft. 


c. g. s. 
Physical 


British 
Engi- 
neering 


Per 
deg. C. 


Per 
deg. F. 


c. g. s. 
Physical 


British 
Engi- 
neering 


"Neat" 

1-2 

1-3 

1-4 

1-5 

1-7 

1-9 
Marble 


110 
110 
110 
110 
110 
110 
110 


1.83 
2.26 
2.28 
2.29 
2.29 
2.23 
2.16 
2.71 


114 
141 
142 
143 
143 
139 
135 
169 


0.00147 
.00344, 
0.00379 
.00352 
.00323 
.00384 
0.00352 
0.00613 


0.356 
0.832 
0.917 
0.852 
0.782 
0.929 
0.852 
1.483 


0.278 
0.216 
0.218 
0.218 
0.217 
0.227 
0.223 
0.213 


0.153 
0.119 
0.121 
0.121 
0.120 
0.126 
0.124 
0.118 


0.00289 
.00705 
0.00762 
0.00705 
0.00650 
0.00758 
0.00732 
0.01059 


0.0204 
0.0492 
0.0533 
0.0493 
0.0455 
0.0530 
. 0509 
0.0739 



Till THKKMAL CONDUCTIVITY AND DIFFUSIVITY OF CONCRETE 



29 



VI. Summary of Results and Conclusions 

11. Summary of Results. — In the following- tables may be found 
a summary of the detailed observations and calculations contained in 
Tables -1 to 11. 

Table 13 gives the average thermal conductivities of the different 
mixtures tested, at different temperatures; the values found in the 
table have been arrived at by collecting and averaging the values given 
in Tables 4 to 11. 

Table 14 gives the average thermal conductivities, at different 
temperatures, for mixtures in which different amounts of water were 

Table 13 

Average Thermal Conductivities of Different Mixtures of Concrete, 

and of Marble, at Different Temperatures 

(Averaged from Tables 3 to 10.) 



Mixture 
By Volumes 


50° C. to 100° C. 
120° F. to 212° F. 


100° C. to 200° C. 
212° F. to 390° F. 


200° C. to 300° C. 
390° F. to 570° F. 


Cement : 
Aggregate 


Cement: 
Sand: 
Gravel 


k 

c. g. s. 

Physical 


k 
British 
Engi- 
neering 


k 

c. g. s. 

Physical 


k 
British 
Engi- 
neering 


k 

c. g. s. 

Physical 


k 
British 
Engi- 
neering 


"Neat" 

1-2 

1-3 

1-4 

1-5 

1-7 

1-9 
Marble 


1-1.2-1.1 

1-1.9-1.7 
1-2.4-2.3 
1-3.1-3.0 
1-4.3-4.0 
1-5.6-5.1 


0.00140 
0.00326 
0.00335 
0.00413 
0.00327 
0.00400 
0.00574 
0.00614 


0.339 

0.789 

0.811 

0.995 

0.791 

0.968 

1.39 

1.49 


0.00163 
0.00344 
0.00379 
0.00352 
0.00323 
0.00384 
0.00352 
0.00493 


0.394 
0.832 
0.917 
0.852 
0.782 
0.929 
0.852 
1.19 


0.00140 
0.00318 
0.00318 
0.00328 
0.00334 


0.339 
0.770 
0.770 
0.794 
0.808 



Table 14 

Variation of Conductivity with Eelative Water Content 

(Summarized from Tables 4 to 9.) 







k in c. g. s. Physical Units 






k in c. g. s. Physical Units 




Relative 
Water 




Mix- 


Relative 
Water 




Mix- 














ture 


Content 


50° C. 


100° C. 


200° C. 


ture 


Content 


50° C. 


100° C. 


200° C. 




Per Cent 


to 


to 


to 




Per Cent 


to 


to 


to 






100° C. 


200° C. 


300° C. 






100° C. 


200° C. 


300° C. 


1:2 


100 


0.00365 


0.00322 


0.00320 


1:5 


100 




0.00353 






110 


0.00300 


0.00332 


0.00310 




110 


0.00381 


0.00380 


0.00380 




120 




0.00317 






120 


0.00273 


0.00305 


0.00270 


1:3 


100 


0.00347 


0.00365 


0.00340 


1:7 


110 


0.00402 


0.00387 






110 


0.00343 


0.00391 






120 




0.00300 






120 


0.00353 


0.00345 


0.00310 


1:9 


110 


0.00573 


0.00359 




1:4 


100 
110 
120 


0.00415 
0.00410 


0.00357 
0.00373 
0.00316 


0.00322 




120 




0.00273 





30 



ILLINOIS ENGINEERING EXPERIMENT STATION 



Table 15 
Effect of Age on Conductivity 
(Summarized from Tables 4 to 9.) 





Relative 




k 

c. g. s. 
Physical 




Relative 




k 

c. g. s. 

Physical 


Mixture 


Water 
Content 
Per Cent 


Age 
Days 


Mixture 


Water 
Content 
Per Cent 


Age 
Days 


1:2 


110 


28 


0.00335 


1:5 


120 


28 


0.00330 






120 


0.00331 






120 


0.00297 


1:3 


110 


28 


0.00398 


1:7 


110 


28 


. 00380 






120 


0.00365 






120 


0.00380 


1:4 


110 


28 


0.00376 


1:9 


110 


28 


0.00340 






120 


0.00337 






120 


0.00387 



used; the values have been arrived at by averaging the values giveu 
in Tables 5 to 10. 

Table 15 gives the average thermal conductivities for mixtures of 
different ages. The values have been obtained for only a few of the 
mixtures, and for one water content only in each case. 

12. General Conclusions. — From Table 13 it can be seen that the 
neat cement had a much lower thermal conductivity than any of 
the sand and gravel concrete mixtures; in fact, the thermal con- 
ductivity of the neat cement is scarcely half that of the 1 :2 mixture. 

In the case of the sand and gravel concrete mixtures, the figures 
in the table also show that there is practically no difference in thermal 
conductivity due to the relative "richness*' or "leanness" in cement 
of a mixture, at any rate for the range of temperature of 100 deg. C. 
to 200 deg. C. The values, as previously noted, are probably more 
accurate for this range than for lower temperatures, on account of the 
number and character of the observations. , 

From the values given in Table 12 for the densities of the various 
materials it can be calculated that the voids in the sand and gravel 
concrete mixture range from 16 to 20 per cent ; while in the case of 
the neat cement the percentage of voids is about 42. It seems probable 
that the proportion of solid material to voids to a large extent deter- 
mines the conductivity, and this accounts for the fact that the thermal 
conducivity of the neat cement is so much lower than that of the con- 
crete mixtures, and that the conductivities of the different mixtures 
are so nearly the same. The same table shows that the thermal con- 
ductivity of a stone, like marble, is much greater than that of a 
concrete mixture. 



THE THERMAL CONDUCTIVITY AND DIFFUSIVITY OF CONCRETE 



31 



The figures given in Table 14 appear to indicate that as far as 
consistency is concerned the maximum thermal conductivity occurs 
with a relative water content of about 110 per cent; for relative 
water contents of 100 or 120 per cent the thermal conductivity is 
generally lower. 

From Table 15 it can be seen that age has little if any effect 
on the thermal conductivity of concrete. If there is any change, 
there is a slight decrease in thermal conductivity with age, but this 
is small, and may be due to very small changes in absolute moisture. 
Most of the cylinders cracked at temperatures under 300 deg. C, 
and that fact limited the range of the investigation. In general, 
the richer mixtures of concrete cracked at lower temperatures than 
the leaner mixtures. The results indicate that there is very slight, 
if any, change of conductivity with change of temperature, for con- 
crete; for marble, there is a marked decrease in conductivity with 
rise of temperature. 

In Table 16 are reproduced the results of the experiments of 
Professor C. L. Norton, to which reference has already been made.* 

Table 16 

Earlier Determinations of Conductivity of Concrete 

(From experiments of Professor C. L. Norton.) 



Temperatures — degrees C. 


Mixture 


k- 


-e. g. s. Physical Unit 


35 


Stone 1-2-5 




0.00216 


50 


Stone 1-2-4 








Not stamped 




0.00110 toU. 00160 


50 


Cinder 1-2-4 




0.00081 


200 


Stone 1-2-4 




0.0021 


400 


Stone 1-2-4. 




0.0022 


500 


Stone 1-2-4 




0.0023 


1000 


Stone 1-2-4 




0.0027 


1100 


Stone 1-2-4, 




0.0029 



Professor Norton's method at the lower temperatures was, as he 
names it, the "flat-plate" method. For the higher temperatures 
he used a cylinder of concrete cast about a steel bar which was 
heated by the passage of a heavy electric current. He gives practi- 
cally no details, describing his investigation ' ' in outline only. ' ' The 
table indicates a small increase of thermal conductivity with increase 
of temperature. As the methods employed in his determinations at 



* Proceedings of National Association of Concrete Users, Vol. VII, article by C. 
Norton. 1911. 



32 ILLINOIS ENGINEERING EXPERIMENT STATION 

lower temperatures are not the same as those for higher temperatures, 
the results are not very conclusive. The values of absolute con- 
ductivity are considerably lower than those found in the present 
investigation, but it is impossible to identify the mixtures used. 

Willard and Lichty* give for the thermal conductivity of a 
1:2:4 concrete mixture the value 8.3 "per 1-inch thickness per sq. 
ft. per 1 deg. F."; this is equivalent to 0.00296 in the c.g.s. physical 
units. The method of determination employed was a "hot-air box 
method," a method specially useful for their purpose in testing 
materials used for the walls of buildings. 

From the present investigation, for the more commonly used 
concrete mixtures, that is, those with proportions of cement to aggre- 
gate of 1 :3 to 1 :7, the following average values of thermal conductiv- 
ity and thermal diffusivity appear established : for the c.g.s. physical 
unit system, for the range of temperature between 50 deg. C. and 200 
deg. C, the average thermal conductivity is 0.00366, and the average 
thermal diffusivity, 0.00719 ; for the British engineering unit system, 
for the range of temperatures between 120 deg. F. and 390 deg. F., 
the average thermal conductivity is 0.901, and the average thermal 
diffusivity, 0.0503. These values are for thoroughly dry concrete, 
of the stone-concrete mixture described. 

"While the values for such physical constants as thermal con- 
ductivity and thermal diffusivity, for a material like concrete, are 
necessarily averages, and subject to the variation of averages, yet 
they are probably as definite as other physical constants for struc- 
tural materials, and particularly so when the average values are 
obtained for a considerable number of specimens, as in this investi- 
gation. 



* "A Study of the Heat Transmission of Building Materials," Unir. of 111. Eng. Exp. 
Sta. Bui. No. 102, 1917. 



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33 



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